Question

The inside perimeter of a running track with semi-circular ends and straight parallel sides is 312 m. The length of the straight portion of the track is 90 m. If the track has a uniform width of 2 m throughout, find its area.

• A. $5166m^2$
• B. $5802.57m^2$
• C. $636.32m^2$
• D. $1273.14m^2$

Answer 1

The correct option is C $636.32m^2$

2 semicircles = 1 circle with equal radius
So $2\pi r=132\Rightarrow 2r=\frac{132}{3.14}=42mdiameter$
Area of track = Area within external border - Area within internal border.
$\Rightarrow \pi ({23}^2-{21}^2)+90\times 46-90\times 42\Rightarrow 88\pi +360\Rightarrow 636.3m^2$